In many uses of alternating current, it is important to make rapid and accurate determinations of power and power factor and of dc and rms values of voltage and current. Where microprocessor controls are used, for example, there is often a window of a small fraction of a second available for the measurement. Until now, however, accurate measurements have not been rapid, and vice versa. One common method of measuring these parameters is based on the heating effect of the waveform. As such, it involves the thermal inertia of a heating element and is therefore inherently slow. Another method is based on sampling the instantaneous value of the waveform at uniform time intervals several times per cycle. To find the dc value of a voltage waveform by this method, for example, one has merely to average the voltage samples, including the polarity sign, over an integral number of cycles. This can be expressed mathematically by equation (1), in which N is the number of sampling intervals used in the calculation. ##EQU1## Similarly, the rms value of voltage can be determined by squaring each voltage sample, averaging the squared values, and taking the square root of the result. An equation expressing this process is: ##EQU2## Unfortunately, while sampling and calculating can be accomplished very rapidly, accurate determination of the parameters by this method requires knowledge of the exact frequency or period of the waveform. In order to sample over an integral number of cycles, the period of the waveform must be an exact multiple of the sampling interval. Otherwise, to minimize the error introduced by sampling over other than exact full cycles, the measurement must normally be extended over a large number of cycles. At the low frequencies common in power distribution, this method becomes far from rapid.
An object of this invention is a precise determination of ac waveform parameters that does not require prior knowledge of the waveform period but yet requires measurement over only a relatively short period of time, which can be as few as two approximate waveform cycles.